1. Field of the Invention
The present invention relates generally to measuring the dielectric constant of a material and, more particularly, to measuring the spatial variation of the dielectric constant.
2. Description of Related Art
The dielectric material needed to construct Continuous Transverse Stub-Electrically Scanned Array (CTS-ESA) radar antennas is barium strontium titanate (BST). Barium strontium titanate is a voltage variable dielectric (VVD) material which can operate from DC to microwave frequencies of 12 GHz and beyond. As used herein, the term microwave frequencies is used in its accepted meaning to correspond to frequency bands at about 1 GHz and above, for example, to about 300 GHz. By voltage variable dielectric is meant a dielectric material having a dielectric constant which varies with applied voltage.
The dielectric constant of BST also varies with position. As used herein, the term "dielectric constant" corresponds to the "real dielectric constant". Accordingly, the real dielectric constant as measured over a region on a given material may vary with the location on that material where the measurement is conducted. Dielectric homogeneity corresponds to the extent to which the real dielectric constant varies with position. In particular, dielectric homogeneity is defined as the measure of the spatial variance of the real dielectric constant of a material. High and low dielectric homogeneity correspond to low and high spatial variance, respectively.
The dielectric homogeneity of a material used to construct a CTS-ESA antenna directly impacts the magnitude of the side lobes in the antenna pattern. High dielectric homogeneity yields low side lobes, while low dielectric homogeneity produces high side lobes. High side lobes are detrimental to antenna performance as less energy is associated with the central beam of the antenna. Side lobes also reduce the antenna's ability to discriminate between a main target and off-axis clutter. Consequently, the characterization of the dielectric homogeneity of the material used to construct a CTS-ESA antenna is important.
Precise high resolution dielectric homogeneity measurements performed at microwave frequencies, however, are not practical, and in many cases, impossible. At low frequencies (i.e., lower than microwave frequencies), guarded electrode capacitance measurements are conventionally used to measure the dielectric constant of materials; see, e.g., ASTM D-150, "Standard Test Methods for A-C Loss Characteristics and Permittivity (Dielectric Constant) of Solid Electrical Insulating Materials," ASTM Standard D 150-87, American Society for Testing and Materials. By guarded electrode capacitance measurement is meant that the capacitance is measured between two electrodes, a guarded electrode and an unguarded electrode, wherein the guarded electrode, in practice, has sides and two ends, and is surrounded on all the sides by a guard electrode which is separated therefrom by a guard gap. Fringing and stray capacitance at the edge (i.e., sides) of the guarded electrode are essentially eliminated by the addition of the guard electrode provided that the guard gap is sufficiently small.
To measure the dielectric constant or the permittivity of a material, a test specimen of the material is placed between the guarded electrode and the unguarded electrode and the capacitance therebetween is measured. (As used herein, "permittivity" corresponds to the "real permittivity".)
The capacitance measurements which are conventionally employed are separated into two categories: contact and non-contact. Contact methods employ electrodes which are in direct mechanical contact with the test specimen. Non-contact methods employ electrodes which do not contact the test specimen.
Contact methods are the most commonly employed means for measuring the dielectric constant or the permittivity of a material. With contact methods, the dielectric constant is determined directly from a capacitance measured between a pair of electrodes. However, it is difficult to avoid an air gap between the electrodes and the test specimen when rigid electrodes and a rigid test specimen are used. Additionally, the effect of such an air gap becomes greater as the permittivity of the material being tested increases and the thickness of the test specimen decreases.
Consequently, the rigidity and high permittivity of BST requires that for BST-based materials, vacuum deposited electrodes are employed. Vacuum deposited electrodes are formed directly on the test specimen (e.g., by sputtering or evaporation, etc.) and, thus, avoid the formation of an air gap. Accordingly, to determine the dielectric homogeneity, multiple capacitance measurements are performed using a plurality discrete guarded electrodes which are metallized directly onto the surface of the BST. In particular, metal such as gold and/or silver is deposited on the test specimen thereby forming a metal film. Portions of the metal film are removed to create a plurality of isolated regions in the metal film which serve as the discrete electrodes. Typically a line of metal pads (discrete electrodes) is formed to sample the dielectric constant across the test specimen. This line of discrete electrodes is surrounded by a larger region of metallization which acts as a guard. Individual capacitive measurements are made at each of the metal pads to establish the variation in capacitance across the test specimen. In some cases, in order to further reduce stray capacitance when a capacitance measurement at a given metal pad is taken, any adjacent metal pads (typically two) are electrically connected to the surrounding larger region of metallization using jumpers.
This method of measuring dielectric homogeneity, however, is time consuming; the entire process takes a minimum of four days.
This method of using discrete guarded electrodes to perform multiple capacitance measurements also lacks the desired accuracy in determining the permittivity or dielectric constant. One source of uncertainty in computing the permittivity is in the determination of the dimensions of the individual discrete electrodes. The dimensional variation of the electrodes is a significant source of error associated with this method. Dimensional variations of the test specimen will also affect the accuracy of the measurements (as is true for all techniques), however, the test specimens are typically ground with tight dimensional tolerances, e.g., .+-.0.0001 inch (0.0025 mm) for a given lot.
Another source of error originates from stray capacitance. To conduct each capacitance measurement, electrical connection to the electrodes is completed using a four point probe or wires attached to each of the discrete guarded electrodes. A four-point probe is the preferred means of electrical connection. Both four-point probes and attached wires, however, produce stray capacitance. Disadvantageously, the stray capacitance associated with each of the guarded electrodes is different. In the case of the four-point probe, the inconsistencies in the stray capacitance result from moving the probe and/or the test specimen as each discrete electrode is tested. Stray capacitance can be a significant source of error since the values of capacitance to be measured are small, i.e., in the same range as the noise produced by the stray capacitance. Due to the uncertainty in the dimensions of the individual electrodes and to the inconsistent stray capacitance associated with each individual electrode, the dielectric homogeneity, as determined using this method, lacks the desired accuracy.
Additionally, positioning restrictions for the discrete guarded electrodes limit the spatial resolution of the dielectric homogeneity measurements. Typically, it is desirable to have the guard electrode extend beyond the guarded electrode by at least twice the thickness of the test specimen. Consequently, the guarded electrodes must be spaced apart by a distance that is greater than twice the thickness of the test specimen. Such spacing requirements restrict the placement of each of the discrete guarded electrodes. The resolution of the measurement of the dielectric homogeneity is thus limited. (It will be appreciated that when electrical jumpers are used to electrically connect adjacent metal pads to the surrounding larger region of metallization, the guard electrode need not necessarily extend beyond the guarded electrode by at least twice the thickness of the test specimen. However, in this case where jumpers are employed and the guard electrode does not extend beyond the guarded electrode by at least twice the thickness of the test specimen, then some uncertainties may exist in the capacitance measurements.)
Alternatively, non-contact methods can be used to measure the dielectric constant of materials at low frequency (i.e., lower than microwave frequencies). Non-contact methods include fluid displacement methods wherein multiple capacitance measurements (at least four) are obtained using two or more dielectric fluids or liquids; see, e.g., H. S. Endicott et al, "Measurement of Permittivity and Dissipation Factor Without Attached Electrodes", in 1960 Annual Report, Conference on Electrical Insulation, NAS-NRC Publication 842, 1961, pp. 19-30 and W. P. Harris et al, "Precise Measurement of Dielectric Constant by the Two-Fluid Technique", in 1962 Annual Report, Conference on Electrical Insulation, NAS-NRC Publication 1080, 1963, pp. 51-53. For example, a test specimen is introduced into a cell filled with a dielectric fluid and the change in capacitance is determined, first when the cell is filled with a dielectric fluid having a low permittivity and second when the cell is filled with a dielectric fluid having a higher permittivity. The permittivity of the specimen is calculated using the permittivities of the two dielectric fluids and the two capacitances changes.
Fluid displacement methods, however, involve placing the test specimen between electrodes and then removing the specimen. This process can result in misalignment and, thus, affect the accuracy of the calculated location and value of permittivity measured. Fluid displacement methods are also time consuming since they require changing the dielectric fluid.
An additional non-contact method used to measure the dielectric constant of liquids at low frequency is reported by, e.g., I. Yu, "Electrodeless measurement of RF dielectric constant and loss", Measurement Science Technology, Vol. 4, 1993, pp. 344-348.
Some non-contact (or probe-type) methods can measure the permittivity of materials at microwave frequencies. The most common of these non-contact techniques is to employ an open-ended coaxial line sensor such as the HP 85070A dielectric probe available from Hewlett-Packard Company (Santa Rosa, Calif.). Probes of this type, however, suffer large uncertainties when used to conduct measurements on rigid materials having low loss or high permittivity. Difficulties (described above) result from the air gap formed between the probe and the rigid material. The BST-based material for use in fabricating CTS-ESA antennas is a rigid material having low loss and high permittivity. Accordingly, an open-ended coaxial line sensor is not the ideal probe for performing dielectric homogeneity measurements on BST-based material. Additionally, when conducting measurements on low loss materials having finite thickness, and in particular, for thin test specimens, microwave energy can reflect off a back surface thereby confusing the measurement.
Coaxial line probes, and non-contact microwave frequency techniques, in general, suffer additional disadvantages. Other non-contact microwave frequency techniques such as free space techniques are based on directing a microwave beam at or through a slab of material and measuring the reflection and/or transmission coefficients; see, e.g., "Dielectric Materials Measurements: Solutions Catalog of Fixtures and Software", Hewlett Packard Company, Microwave Instrument Division, 1993, pp. 2-21. As a result of fringing and the divergence of the microwave beam, however, these non-contact microwave frequency techniques do not sample a precisely well defined region with uniformly distributed incident microwave energy. These non-contact microwave frequency techniques also lack the desired resolution. Additionally, the orientation of the electric fields associated with the coaxial line probes and the diverging microwave beam include components that are both perpendicular and parallel to the surface of the test specimen. Consequently, these non-contact microwave frequency techniques do not independently sample the components of the dielectric constant perpendicular and/or parallel to the surface (which are different for anisotropic materials). Accordingly, the anisotropic nature of BST-based material can cause erroneous conclusions to be produced when using such non-contact microwave frequency techniques to measure the permittivity or dielectric constant.
Thus, there remains a need for a method for measuring dielectric homogeneity that avoids most, if not all, the foregoing problems.